A note on regular Ramsey graphs

TL;DR

This paper proves the existence of regular triangle-free graphs with bounded independence number, establishing a universal constant that limits the size of independent sets in such graphs.

Contribution

It introduces a new bound on the independence number of regular triangle-free graphs, demonstrating the existence of graphs with specific extremal properties.

Findings

Existence of regular triangle-free graphs with independence number at most C√(n log n)

Establishment of a universal constant C for all natural n

Advancement in understanding extremal properties of Ramsey graphs

Abstract

We prove that there is an absolute constant $C>0$ so that for every natural $n$ there exists a triangle-free \emph{regular} graph with no independent set of size at least $C\sqrt{n\log n}$.